The one monument Berlin's mayor, Klaus Wowereit, would most like to leave his city is the long-delayed Berlin Brandenburg International Airport. But with the city deep in debt and not so much as an earth-digger in place at the site, Berliners do not expect to see BBI in action until 2012 at the earliest.

In the meantime, the city's tiny international airport, Tegel, is stretched to capacity, while Tempelhof, a regional airport just 6km away from the Brandenburg Gate, is scheduled for closure at the end of October. Wowereit is determined to see the end of Tempelhof despite huge protest from Berliners, not to mention the one million passengers and 13 airlines that have used it over the past year. At least one of these airlines, Germania, has offered to buy Tempelhof, but its offer has been turned down. If Wowereit gets his way, in a court decision next month, Tempelhof's fate will be sealed and, along with it, one of the world's most remarkable and likable air terminals.

From an architectural point of view, Tempelhof Weltflughafen - "world airport", as it was optimistically known before the Luftwaffe flew to Warsaw, with no intention of landing, in September 1939 - is a magnificent and compelling enigma. Designed by Ernst Sagebiel (1892-1970) between 1934 and 1936 and built well into the second world war, it was to be the international gateway to Germania: Berlin in its over-inflated postwar guise, as planned by Albert Speer, assuming victory over the Allies by 1948.

Tempelhof Weltflughafen replaced an existing airfield built up from 1923 on the former Prussian military parade ground where Orville Wright had wowed Berliners in 1909 with early flying displays. Located immediately off Speer's proposed grand north-south avenue scything through Berlin, it was to form part of a new city square, giving almost immediate access to the bombastic Nazi ministries that were to rise here on the way to the core of the old Prussian city centre. A few of these were built, including Goering's air ministry, which still stands, stiff and aloof, at the junction of Wilhelmstrasse, the road to Tempelhof, and Leipzigerstrasse. Today it houses the ministry of finance. It, too, was designed by Sagebiel.

Curiously, Sagebiel had run the big and busy Berlin studio of architect Erich Mendelsohn until Mendelsohn, a Jew who had seen the writing on Hitler's neoclassical walls, left Berlin in 1933. Sagebiel moved straight away to design Goering's air ministry, and then Hitler's Tempelhof.

If Sagebiel's career seems contrary, so is the architecture of Tempelhof. As my Crossair Saab 2000 turbo-prop thrums in from Basle, the view is of an unexpectedly beautiful, tree-lined airfield and the great, stretched and curving arms of the 1.2km air terminal. As the aircraft rolls towards Sagebiel's embrace, the airside frontage of the building, adorned with a supremely imposing cantilevered awning under which smaller aircraft park, proves to be every bit as clean-cut and functional as any streamlined building by Mendelsohn. It is only the frontages of the building that echo Hitler and Speer's grandiosity.

Garbed in classical dress, stripped of ornamentation, Tempelhof Zentralflughafen, as it is called today, addresses the streets of Berlin set immediately across from its massive and lofty entrance. In the imagination, it is easy to add Nazi eagles, swastika flags and titanic statuary by Arno Breker to that facade. In reality, this is the most modern and ambitious of all 1930s airports; it wears what is really quite regular Prussian, or Berlin, uniform. There are many buildings in the city, notably those of the renowned Karl Friedrich Schinkel (1781-1841), that are equally severe. Sagebiel's vigorous nods to classicism here are no more or less deferential than those of contemporary Scandinavian architects - such as the great Gunnar Asplund, who practised an equally powerful classical style, stripped to its elements, and much praised today.

Whatever you might feel about its style, Tempelhof is one of the easiest city airports to use. Passengers step down from the aircraft, walk straight into the terminal, out through its magisterial central lobby and into the city in a matter of minutes. You can get to a meeting in central Berlin in less time than it takes to negotiate your way out of the purgatorial sprawl of Heathrow. Even London's City airport, a fairer comparison, takes a long time to get to and, riverside setting apart, has little of the sense of occasion of Tempelhof.

When I arrived on a sweltering evening last week, I was swept up by Alexander Beljatzsky, an enthusiastic young Berlin architect who is one of the driving forces behind the campaign to save the airport. Touring the building with a party of local businessmen and women, I was captivated by its bravura and practical design, and by the daring of its innovative architecture. I learned that Tempelhof was incomplete by the time Hitler invaded Poland, and that the 80,000-strong crowds who were to have sat in tiers on its 1.2km of roof, gained by 15 sentry-like stone stair-towers, to watch Goering's finest performing air displays, never came. Instead, forced labour was used to continue building work while Ju-87 dive-bombers and Fw-190 fighters were assembled in the concrete railways and road tunnels running beneath the terminal.

Seized and damaged by the Red Army in 1945, Tempelhof was taken over by the Americans, who completed Sagebiel's design in the 1950s. In 1948-49, Tempelhof was the focal point of the Berlin Airlift, when Douglas C-47s and C-54s shipped food and other supplies into a Berlin besieged by Stalin. Its Nazi origins were redeemed.

The era of big commercial jets has been less kind to Tempelhof, diverting traffic to Tegel and Schönefeld further afield. Yet Tempelhof remains the inner-city airport par excellence. Here small, quiet aircraft dart in and out to and from destinations throughout Germany, Belgium and Switzerland, as do swarms of executive jets and tiny piston-engined machines.

Sagebiel's all-embracing terminal building includes hangars for storage and maintenance, the distribution of freight and airline offices as well as the remains of what were to have been a huge restaurant, ballroom and rooftop beer garden. Some of the offices are now the studios of architects such as Beljatzsky; the whole complex could very easily, with a little imagination, be transformed into a successful airport laced through with hi-tech and aero-industry concerns, together with business offices.

But for whatever reason, Wowereit and his SDP colleagues want to strip Berlin of this peerless asset. Local people, for whom Tempelhof is a source of work in a city with a high rate of unemployment, want the airport to remain. As tests have proved, it is not even noisy. In fact, from the surrounding streets, the sound of traffic drowns out the the buzz of piston engines and the occasional whoosh of a Boeing 737.

If it is closed, Tempelhof will be a vast mill around the city's neck. A listed building that the federal government refuses to take under its wing if air traffic should end, it will sit all but empty, making huge losses and rotting simply to satisfy a political whim and to ensure that all eyes are on the new Berlin Brandenburg International Airport, miles and many years away.

Other European cities would be only too pleased to have an airport like Tempelhof, and many Berliners hope that international pressure might yet come to its rescue. Sagebiel's airport has long since lost its Nazi associations. It is a brilliant design threaded carefully into the city it continues - and should continue - to serve.

· There are no direct flights from British airports into Berlin Tempelhof. To take a guided tour of the airport, call 0049 30 6091 1628.